Dynamic beaters are actuators in widespread use in industry for preventing vibration from propagating in a given structure:                eliminating vibration at a given frequency (e.g. for a rotary machine);        damping a natural mode of the structure that can be excited either by harmonic type vibration or by random/impact type vibration.        
They operate on the principle of a spring-mass unit. There are several major parameters for beaters:                mass M;        tuned frequency f0;        quality factor Q.        
A beater is characterized by its mechanical impedance Z at its fixing interface with the base (or host) structure that is to be damped.
The following notation is used:                F: connection force between the base structure and the beater;        v: the vibratory speed at the point of connection between the base structure and the beater;        Z=F/v then gives the mechanical impedance of the beater, and this characteristic is independent of the base structure.        
It can be shown that the complex impedance of the beater can be written as follows (where p is the Laplace variable: p=j★ω):       Z    B    =            M      *      p      *              (                  Q          +                      p                          ω              0                                      )                            Q        ⁡                  (                      1            +                                          p                2                                            ω                0                2                                              )                    +              p                  ω          0                    having modulus:           Z        =            M      *      w      ⁢                                    Q            2                    +                                    w              2                                      ω              0              2                                                                                              Q              2                        ⁡                          (                                                1                  -                                      w                    2                                                                    w                  0                  2                                            )                                2                +                              ω            2                                ω            0            2                              with:                ω=2π★f, where f is the disturbing frequency;        ω0=2π★f0 the natural angular frequency of the beater: ω02=K/M        
Q is related to the stiffness and the damping by:
Type of dampingViscous (C)With hysteresis  Q  =            KM        C    Q  =      1    η  
It can be shown that the maximum value of this impedance is given by:ZB=M★ω0√{square root over (1+Q2)}≈M★ω0★Q for Q≧3 